The Bank of Japan, sometimes dubbed the "Tokyo whale" because of its huge influence on the country's stock market, may be about to change its habits because it's taking up too much of the pool.

That's the speculation after local press reported that the central bank is considering changing how it buys shares through its exchanged-traded fund program.

At its two-day meeting starting Monday, Gov. Haruhiko Kuroda's BOJ will discuss reducing investments in ETFs tracking the 225-issue Nikkei average, the old blue-chip gauge, because its purchases are having an outsize impact on its companies, the Nikkei newspaper reported last week. Instead, it will buy more funds tracking the broader Topix index, it said.